Thermally compensated optical diffraction gratings

Abstract

An optical diffraction grating includes a substantially transparent grating substrate which has substantially flat first and second surfaces, and a set of grating lines on the first surface characterized by a grating spacing Λ. The grating substrate has a temperature-dependent refractive index n sub and is immersed in a medium having a temperature-dependent refractive index n med . The first and second substrate surfaces are non-parallel and form a dihedral angle α. The gratings lines are substantially perpendicular to a plane of incidence defined by surface-normal vectors of the first and second surfaces. Variation of a diffraction angle θ d′ with temperature, exhibited by the optical diffraction grating at a design wavelength λ and at a design incidence angle θ in in the plane of incidence, is less than that variation exhibited by a reference diffraction grating that has parallel first and second substrate surfaces but is otherwise identical to the optical diffraction grating.

What is claimed is: 
     
       1. An optical diffraction grating comprising:
 a grating substrate having substantially flat first and second surfaces, which substrate is substantially transparent over an operational wavelength range that includes a design wavelength λ, has a temperature-dependent refractive index n sub , and is immersed in a medium having a temperature-dependent refractive index n med ; and 
 a set of grating lines formed in or on the substrate that are substantially parallel to the first substrate surface and characterized by a grating spacing Λ, 
 wherein: 
 the first and second substrate surfaces are non-parallel and form a dihedral angle α; 
 the gratings lines are substantially perpendicular to a plane of incidence defined by surface-normal vectors of the first and second substrate surfaces; 
 the optical diffraction grating is arranged as a reflection grating arranged to diffract, at a diffraction anile θ d′  with resect to the second surface, at least a portion of an optical signal at the design wavelength λ that is incident on the second surface at a design incidence angle θ in  in the plane of incidence, and 
 variation of the diffraction angle θ d′  with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at the design incidence angle θ in  in the plane of incidence, is less than that variation exhibited by a reference diffraction grating that has parallel first and second substrate surfaces but is otherwise identical to the optical diffraction grating. 
 
     
     
       2. The optical diffraction grating of  claim 1  wherein the grating substrate comprises first and second grating substrate members, the first grating substrate member has substantially parallel first and second surfaces and the set of grating lines formed on its first surface, the second substrate member has non-parallel first and second surfaces that form the dihedral angle α, the first and second substrate members are assembled with one surface of the first substrate member against one surface of the second substrate member, and the temperature-dependent refractive index n sub  is the refractive index of the second substrate member. 
     
     
       3. The diffraction grating of  claim 1  wherein the angle α results in a first derivative of diffraction angle θ d′  with respect to temperature that is less than about 0.000001° per ° C. at a design temperature T 0 , the design wavelength λ, and the design incidence angle θ in . 
     
     
       4. The diffraction grating of  claim 1  wherein the variation of a diffraction angle θ d′  with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at a design incidence angle θ in  in the plane of incidence, is less than about 0.00001° over an operational temperature range. 
     
     
       5. The diffraction grating of  claim 1  wherein the grating substrate comprises fused silica, the medium comprises ambient air, and the angle α is between about 2.0° and about 2.5°. 
     
     
       6. The diffraction grating of  claim 1  wherein the grating substrate comprises fused silica, the medium comprises ambient air, the angle α is between about 2.0° and about 2.5°, the grating spacing is between about 800 nm and about 2000 nm, and the operational wavelength range is between about 1200 nm and about 1700 nm. 
     
     
       7. A method comprising:
 forming a grating substrate having substantially flat first and second surfaces, which substrate is substantially transparent over an operational wavelength range that includes a design wavelength λ, has a temperature-dependent refractive index n sub , and is immersed in a medium having a temperature-dependent refractive index n med ; and 
 forming a set of grating lines in or on the substrate that are substantially parallel to the first substrate surface and characterized by a grating spacing Λ, 
 wherein: 
 the first and second substrate surfaces are non-parallel and form a dihedral angle α; 
 the gratings lines are substantially perpendicular to a plane of incidence defined by surface-normal vectors of the first and second substrate surfaces; 
 the optical diffraction grating is arranged as a reflection grating arranged to diffract, at a diffraction angle θ d′  with respect to the second surface, at least a portion of an optical signal at the design wavelength λ that is incident on the second surface at a design incidence angle θ in  in the plane of incidence, and 
 variation of the diffraction angle θ d′  with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at the design incidence angle θ in  in the plane of incidence, is less than that variation exhibited by a reference diffraction grating that has parallel first and second substrate surfaces but is otherwise identical to the optical diffraction grating. 
 
     
     
       8. The method of  claim 7  wherein the grating substrate comprises first and second grating substrate members, the first grating substrate member has substantially parallel first and second surfaces and the set of grating lines formed on its first surface, the second substrate member has non-parallel first and second surfaces that form the dihedral angle α, the first and second substrate members are assembled with one surface of the first substrate member against one surface of the second substrate member, and the temperature-dependent refractive index n sub  is the refractive index of the second substrate member. 
     
     
       9. The method of  claim 7  wherein the angle α results in a first derivative of diffraction angle θ d′  with respect to temperature that is less than about 0.000001° per ° C. at a design temperature T 0 , the design wavelength λ, and the design incidence angle θ in . 
     
     
       10. The method of  claim 7  wherein the variation of a diffraction angle θ d′  with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at a design incidence angle θ in  in the plane of incidence, is less than about 0.00001° over an operational temperature range. 
     
     
       11. The method of  claim 7  wherein the grating substrate comprises fused silica, the medium comprises ambient air, and the angle α is between about 2.0° and about 2.5°. 
     
     
       12. The method of  claim 7  wherein the grating substrate comprises fused silica, the medium comprises ambient air, the angle α is between about 2.0° and about 2.5°, the grating spacing is between about 800 nm and about 2000 nm, and the operational wavelength range is between about 1200 nm and about 1700 nm. 
     
     
       13. A method comprising directing an input optical signal onto an optical diffraction grating at a design incidence angle θ in  so that a portion of the input optical signal is diffracted as an output optical signal at a diffraction angle θ d′ , wherein:
 the optical diffraction grating comprises (i) a grating substrate having substantially flat first and second surfaces, which substrate is substantially transparent over an operational wavelength range that includes a design wavelength λ, has a temperature-dependent refractive index n sub , and is immersed in a medium having a temperature-dependent refractive index n med , and (ii) a set of grating lines formed in or on the substrate that are substantially parallel to the first substrate surface and characterized by a grating spacing Λ; 
 the first and second substrate surfaces are non-parallel and form a dihedral angle α; 
 the gratings lines are substantially perpendicular to a plane of incidence defined by surface-normal vectors of the first and second substrate surfaces; 
 the input optical signal is incident on the second surface at the design incidence angle θ in , 
 the optical diffraction grating is arranged as a reflection grating arranged to diffract, at the diffraction anile θ d′  with resect to the second surface, at least a portion of the optical signal at the design wavelength λ that is incident on the second surface at the design incidence angle θ in  in the plane of incidence, and 
 variation of the diffraction angle θ d′  with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at the design incidence angle θ in  in the plane of incidence, is less than that variation exhibited by a reference diffraction grating that has parallel first and second substrate surfaces but is otherwise identical to the optical diffraction grating. 
 
     
     
       14. The method of  claim 13  wherein the grating substrate comprises first and second grating substrate members, the first grating substrate member has substantially parallel first and second surfaces and the set of grating lines formed on its first surface, the second substrate member has non-parallel first and second surfaces that form the dihedral angle α, the first and second substrate members are assembled with one surface of the first substrate member against one surface of the second substrate member, and the temperature-dependent refractive index n sub  is the refractive index of the second substrate member. 
     
     
       15. The method of  claim 13  wherein the angle α results in a first derivative of diffraction angle θ d′  with respect to temperature that is less than about 0.000001° per ° C. at a design temperature T 0 , the design wavelength λ, and the design incidence angle θ in . 
     
     
       16. The method of  claim 13  wherein the variation of a diffraction angle θ d′  with temperature, exhibited by the optical diffraction grating at the design wavelength λ and at a design incidence angle θ in  in the plane of incidence, is less than about 0.00001° over an operational temperature range. 
     
     
       17. The method of  claim 13  wherein the grating substrate comprises fused silica, the medium comprises ambient air, and the angle α is between about 2.0° and about 2.5°. 
     
     
       18. The method of  claim 13  wherein the grating substrate comprises fused silica, the medium comprises ambient air, the angle α is between about 2.0° and about 2.5°, the grating spacing is between about 800 nm and about 2000 nm, and the operational wavelength range is between about 1200 nm and about 1700 nm.